Fifteen games versus the dregs allowed the Yankees to wake up. Now it’s time to show the baseball world the Bombers have the ability and desire to start putting the Red Sox to sleep in the AL East.

Beginning with today’s 4:05 p.m. start at Yankee Stadium, the Yankees and Red Sox will play four pressure-packed games in front of sold-out crowds that will be into each and every pitch. It’s July 4, and nobody talks about the season being young anymore. There are less than three months to decide who’ll win the East, a division the Yankees have copped the past five years.

After going 12-3 against the Devil Rays, Mets and Orioles, the Yankees take a step up in class against the Red Sox, who are four games behind in second place after losing to Tampa Bay 6-5 last night, still trying to figure out how to close games.

For all the unrest the Yankees bullpen has gone through this year due to injuries (Mariano Rivera, Antonio Osuna) and ineffectiveness (Juan Acevedo), the Red Sox’s ill-advised bullpen-by-committee has been shakier.

Red Sox-Yankees in The Bronx on a holiday weekend! Sometimes, the schedule maker gets it right.

“The fans get going, the adrenaline is kicking in. and you’re feeling good,” said Rivera, who gives the Yankees a huge edge in the late innings. “You don’t want to lose the game.”

Listen closely and you almost can hear the first strains of “Boston [Stinks]!” leaking out of the Stadium. By the time David Wells throws today’s first pitch, the crowd will be over the top in every way.

Players often talk of how they don’t worry about where other teams are in the standings. “If we take care of ourselves . . .” is the usual refrain. Not this weekend.

“They are in second place so it’s an important series,” Jorge Posada said. “If they were in last place, it might be a little different. But they are right behind us. It’s going to be very important.”

A Yankees sweep and their lead would swell to eight games. Get swept, and they would be tied for first. No longer does either side have to glance at a scoreboard to see what’s happening to the other.

“The fact that you’re playing the Red Sox when they’re the ones sitting behind you, every game you play is double. So you don’t worry about the scoreboard, they are in the ballpark with you,” said Joe Torre, whose club is 4-2 against the Red Sox this year.

“You need to beat them in order to make them basically win twice when they leave. I think that’s important. And if you are ever going to cut into a lead, that’s the way to do it, when you play head-to-head.”

Torre and the Yankees don’t have their fingers crossed for two wins. Not with their four top starters – David Wells, Roger Clemens, Andy Pettitte and Mike Mussina – going.

“You can’t go in there thinking in terms of, ‘All we need is a split,’ ” Torre said. “To me, that’s a negative. And even winning three of four is a negative. When it’s over, you see how it turned out. But you certainly need to pay attention to every single inning of every game. I know it sounds a little boring, but that’s basically what you need to do. You need to play every game because they are all important.”

It’s not the Yankees’ style to brag. But with Jason Giambi and Hideki Matsui smoking at the plate, Alfonso Soriano showing signs he is coming out of a slump, and Rivera throwing better than Torre has ever seen him, the confidence they lost in May is back.

Now it’s time for them to show everybody they are ready to grab the AL East by the throat.

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Tale of the tape

The Yankees and Red Sox have met six times this season, with the Yankees winning four times.

Here’s a look at the stats from those meetings heading into this weekend’s series at the Stadium: